Duopoly

du·op·o·ly

d(y)o͞oˈäpəlē

Among Fifty Most Populous Countries, U.S. and Nigeria are the Only Nations with Two Parties in Lower House of National Legislature

http://ballot-access.org/2015/04/12/among-fifty-most-populous-countries-u-s-and-nigeria-are-the-only-nations-with-two-parties-in-lower-house-of-national-legislature/

Two-party system

Modern American politics, in particular the electoral college system has been described as duopolistic since the Republican and Democratic parties have dominated and framed policy debate as well as the public discourse on matters of national concern for about a century and a half. Third Parties have encountered various blocks in getting onto ballots at different levels of government as well as other electoral obstacles, more so in recent decades.

There is strong agreement that the United States has a two-party system; historically, there have been few instances in which third party candidates won an election...

Siterunner correction: More than a "few instances" -- in the US there have been and are currently hundreds of examples of third party candidates who have won an election, or have been appointed and confirmed to office, at the local and state levels of government

It is at the federal level and in races for President where the existing ballot access laws, constraints, practices and restrictions act to limit effective participation by independent third parties/minor parties, although for a number of decades polls have indicated that approximately 30+ percent of US citizen voters consider themselves "independents" and choose not to align themselves with either of the two major parties

https://en.wikipedia.org/wiki/Two-party_system